i is useful because it lets you convert cos(x) and sin(x) into exponential forms.

The thing on the left can be turned into the things on the right, which although they may look more complicated can make various bits of maths a lot easier. When it was invented, i was a curiosity, but it actually has a lot of uses.

If you were being serious, Selmac, I hope that was slightly enlightening. If you were joking; reading that was your punishment. Why on Earth would I want to do any maths? Studying Physics tends to require it a bit.